Near-infrared studies of glucose and sucrose in aqueous solutions:
water displacement effect and red shift in water absorption from
water-solute interaction
Youngeui Jung1 and Jungseek Hwang1,2,∗
arXiv:1310.0687v1 [cond-mat.mtrl-sci] 2 Oct 2013
1
Department of Physics, Pusan National University, Busan 609-735, Republic of Korea
2
Department of Physics, Sungkyunkwan University,
Gyeonggi-do, Suwon 440-746, Republic of Korea and
∗
Corresponding author: [email protected]
We use near infrared spectroscopy to obtain concentration dependent glucose
absorption spectra in their aqueous solutions in the near-infrared range (3800 7500 cm−1 ). We introduce a new method to obtain reliable glucose absorption
bands from aqueous glucose solutions without measuring the water displacement coefficients of glucose separately. Additionally, we are able to extract
the water displacement coefficients of glucose, and this may give a new general method using spectroscopy techniques applicable to other water soluble
materials. We also observe red shifts in the absorption bands of water in the
hydration shell around solute molecules, which comes from contribution of the
interacting water molecules around the glucose molecules in solutions. The
intensity of the red shift get larger as the concentration increases, which indicates that as the concentration increases more water molecules are involved
in the interaction. However, the red shift in frequency does not seem to depend significantly on the concentration up to our highest concentration. We
also performed the same measurements and analysis with sucrose instead of
glucose as solute and compare.
c 2013 Optical Society of America
OCIS codes: 300.6340, 300.1030
1
Index Headings:
Near infrared spectroscopy, Water displacement coefficient, Glucose
solution, Sucrose solution
INTRODUCTION
The possibility of providing a direct, non-invasive approach to measuring glucose concentrations in blood has inspired studies of the applications of infrared spectroscopy for
analyte detection in various solutions. It has been shown that glucose has many distinct
infrared (IR) absorption features in the far-infrared (FIR),[1–3] mid-infrared (MIR),[4–8]
and near-infrared (NIR)[9–15] regions. However, water, the main component of blood, also
displays strong IR absorption features in these regions, with increased absorption as you
move further towards FIR. Water absorption modes in a wide spectral range can be found
in a literature.[16]
In studies dealing with MIR analyte detection in blood,[4, 5] the experiments were
performed on dry samples or using second derivative spectra to obtain concentration
dependence.[7] This causes a large inaccuracies due to an increase in noise because of derivation. Water IR absorption in the MIR region as well as the FIR is overwhelming,[17] rendering non-invasive glucose detection at physiological concentrations extremely difficult due to
high water content in blood. In a recent work,[14] glucose absorption bands were extracted
by using an independently measured water displacement coefficient of glucose. The water
displacement coefficient is a measure of the second order effect of the presence of glucose
on the spectrum of water. Since, at physiologically relevant concentration of glucose in
blood, the water bands are orders of magnitude stronger than the glucose bands, incorrect
treatment can be a major source of error.
In this study we introduce a new method to obtain reliable glucose absorption bands
without measuring the water displacement coefficient separately. Because there is a strong
water absorption peak at 5200 cm−1 and almost no or negligible glucose absorption at
this frequency, we take advantage of this strong and isolated water absorption peak to
remove water absorption from the measured transmission of aqueous glucose solutions. By
adjusting effective thicknesses of water in a liquid cell to match the amplitude of the water
peak for six different glucose solutions in the same liquid cell we are able to remove water
absorption bands accurately and to extract an accurate concentration dependent glucose
absorption coefficient in solution. Additionally, we are able to obtain a water displacement
2
coefficients of glucose by using the concentration dependent effective thickness of water
in the cell. We also observe red shifts in the absorption bands of water in the solution.
Similar there are red shifts from interacting water in macroscopic air-water and oil-water
interfaces and in the hydration cell around nonpolar hydrocarbon solute groups.[18, 19]
Water structure enhancement within hydration shells was reported.[20, 21] This indicates
that water molecules around solute molecules are not free; they are interacting with solute
molecules. Our analysis shows that the number of interacting water molecules seems to
increase as the concentration of solute increases. We also apply the same method to another
water soluble material, sucrose, which has a higher molecular weight than glucose. We
compare the results of sucrose with those of glucose.
EXPERIMENTS
We prepared six different aqueous glucose and six sucrose solutions: the concentrations
were 1.00, 2.00, 4.00, 6.00, 8.00 and 10.00 g/dL. All solutions were prepared using anhydrous D-(+)glucose (C6 H12 O6 ) purchased from Sigma-Aldrich (USA), sucrose (C12 H22 O11 )
purchased from Junsei Chemical (Japan), and grade-3 deionized water. Aqueous samples
were placed in a 250 ±10 µm path-length liquid cell composed of glass. The cell was made
using epoxy glue to attach 155 µm thick pieces of microscope cover glass (Sargent-Welch,
USA) to a 1-mm thick microscope slide (VWR Scientific, USA) forming a rectangular chamber (∼0.250×11.2×17.5 mm3 ). By covering this with another microscope slide we created a
250 ±10 µm thick liquid cell appropriate for aqueous sample measurements. Reproducibility
and stability of the measurement system were tested before proceeding with the study. We
also prepared a pure amorphous glucose pellet and a sucrose pellet melting the D-glucose
and sucrose powders, respectively. We measured those pellets to obtain the absorption
coefficients of pure glucose and sucrose.
A commercial Fourier transform infrared (FTIR) spectrometer, Bruker Vertex 80v was
used for collecting near infrared spectra. The optical setup consists of a 75 W tungsten
lamp as a light source, a CaF2 beam splitter, and a room temperature deuterated triglycine
sulfate (DTGS) detector. We measured transmittance spectra, T (ω), of samples on a
sample holder with a 5.0 mm diameter circular aperture and a resolution of 5 cm−1
over a range of 3800 - 7500 cm−1 . An empty glass cell was used as the reference for all
transmittance measurements except for the amorphous glucose and sucrose pellets. To
3
get transmittances of the two pellets an empty hole was used as the reference. We note
that for all transmittance measurements of liquid samples we used the same liquid cell.
All transmittance spectra were taken at room temperature (23 o C). Absorption coefficient
spectra, α(ω), were calculated from measured transmittances.
MEASURED DATA AND ANALYSIS
We measured transmittance spectra of the six different glucose and six sucrose solutions
and pure water in the cell as well as pure amorphous glucose and sucrose pellets. The
absorption coefficient can be extracted from a measured transmittance spectrum by using
the well-known Beer-Lambert’s formula:
α(ω, C) = −
ln T (ω, C)
d
(1)
where α(ω) is the absorption coefficient, T (ω) is the measured transmittance, C is the
concentration of the solution and d is the thickness of the sample. Figure 1 shows raw
absorption coefficients for the six glucose solutions, pure water, and a pure amorphous
glucose pellet. For the solution samples (water and solutions) we used the same thickness
d0 ∼
= 252 µm since we used the same liquid cell. We also show a water absorption peak
at 5200 cm−1 , which is a Lorentzian function. Since glucose absorption in the solution is
very weak compared with the water absorption at these concentrations, we can not see large
differences among in solution spectra. In these solution spectra, we observe three strong
water absorption peaks in a spectral range between 3800 and 7500 cm−1 , which are near
4000, 5200, and 6900 cm−1 . There are two physiologically relevant windows in the water
absorption through this measured spectral range; one between 4000 cm−1 and 5200 cm−1 is
the combination region where four distinct glucose peaks are visible and the other between
5200 cm−1 and 6900 cm−1 is the first overtone region where two broad glucose peaks which
are not as distinct or strongly absorbing as those in the combination region.
To obtain the absolute magnitude of glucose absorption from a glucose solution, we
initially subtracted the measured water absorption coefficient from that of each solution. As
a first approximation, we assumed that the thicknesses of water are the same. Then we can
formulate the subtraction procedure as follows:
αsol (ω, C) − αw,d0 (ω) = −
ln[Tsol (ω, C)] h ln[Tw (ω)] i
− −
d0
d0
4
(2)
150
A
130
A
pure water
glucose 1 g/dL (0.056 M)
glucose 2 g/dL (0.111 M)
glucose 4 g/dL (0.222 M)
glucose 6 g/dL (0.333 M)
glucose 8 g/dL (0.444 M)
glucose 10 g/dL (0.556 M)
pure glucose
-1
water peak @ 5210 cm
120
5100 5150 5200
100
-1
α(ω) (cm )
110
30
B
28
50
26
24
4700
4750
4800
0
4000
5000
6000
7000
-1
Frequency, ω (cm )
Fig. 1. (Color online) Absorption coefficients of a pure amorphous glucose (dotted dark blue
line) a pure water (dash-dotted orange line), and six glucose aqueous solutions (from top to
bottom; from low to high concentrations). We also show a water peak at 5210 cm−1 (green
dashed line). In the inset A and B we show expanded views near 5150 cm−1 and 4750 cm−1
respectively.
where d0 is the thickness of our liquid cell. αsol (ω) and αw,d0 (ω) are respectively the absorption coefficients of a solution and pure water calculated using the cell thickness d0 = 252
µm. Tsol (ω) and Tw (ω) are the measured transmittance spectra of the solution and pure
water, respectively. Figure 2 (a) shows spectra resulting from this analysis procedure. There
is only one clearly visible glucose peak at 4700 cm−1 , offset from the actual peak position
seen in figure 1 of 4740 cm−1 . Also, at 5200 cm−1 , there is a sharp downward peak, with the
larger peak for the higher concentrated solution. This concentration dependent downward
peak appears in the difference spectra because we did not consider the water displacement
effect due to the glucose presence in the solution. When glucose is dissolved in water the
volume of the solution changes because each glucose molecule takes up a finite space. We
have to take into account this (water displacement) effect to subtract an appropriate water
spectrum from the solution spectra.
Our approach for solving the downward peak problem in the difference spectra shown
in figure 2 (a) is as follows. There is absence or very weak absorption of glucose around
5
5200 cm−1 , where water has a very strong absorption peak. It means that at that frequency
absorption values of all solutions including pure water should be the same if we use a proper
thickness of water for each solution. We performed the following procedure to remove
an appropriate water absorption from the total absorption of each solution; by adjusting
the thickness of pure water so that its absorption value at 5200 cm−1 is the same as the
absorption value of each solution, we can then subtract a proper water spectrum from each
solution spectrum to obtain pure glucose absorption due to glucose alone in each solution.
We call the proper thickness of water for each solution the effective thickness of water. The
procedure can be formulated as follows:
αsol (ω, C) − αw,def f (ω) = −
ln[Tsol (ω, C)] h ln[Tw (ω)] i
− −
d0
def f (C)
(3)
where def f (C) is the effective thickness of pure water for each concentration and αw,def f (ω)
is the absorption coefficient of water calculated using the effective thickness def f (C), which
is dependent of the concentration. By performing the procedure, the concentration dependent negative peak, that was caused by subtracting too much water absorption, is removed
although not completely. We will discuss this remaining downwards peak in the following
paragraphs. This uncovers new absorption peaks due to glucose that agree with the pure
glucose absorption shown in figure 1, the dotted dark blue curve. The resulting absorption
spectra due to glucose in six solutions are shown in figure 2 (b). In contrast to the single
peak evidence in figure 2 (a) at 4700 cm−1 , three others are obvious in the combination
region and two in the first overtone region. Also, the peak centered at 4700 cm−1 in figure
2 (a) has undergone a shift to the actual peak position of glucose at 4740 cm−1 . Glucose
absorption bands in the first overtone region were also uncovered (see in the inset of figure
2 (b)), displaying absorption at 5700 and 6360 cm−1 . We note that the relative intensities
of the glucose peaks are revealed as well. The concentration dependent peak heights of the
four peaks in the combination region are displayed in figure 5 (a). They show an almost a
linear dependence on concentration.
In the inset of figure 2 (b) the peaks centered at 5700 and 6360 cm−1 have some visible
discrepancies showing variation from the expected concentration dependence. In the first
overtone region it seems that the 4 g/dL solution (green curve) has a larger absorption
value than 6 g/dL (blue curve). However, looking at the 6 g/dL peak, it has a betterdefined shape. Even though the 4 g/dL solution has a higher absorption value, the 6 g/dL
6
solution has a more well-defined absorption compared to its average height in the first
overtone region indicating a stronger real absorption. The same can be said for the 2 g/dL
absorption (red curve) due to glucose, which appears to have a lower absorption than the 1
g/dL solution (black curve) in this region. Even though the area under the curves suggests
that some weaker solutions have stronger absorption, the shape of the absorption peaks
gives additional information about the concentration and a more accurate depiction of the
concentration dependence in the first overtone region. These results can be attributed to
the broader absorption peak of glucose in this region.[14] Due to a broader or worse defined
peak, it is more difficult to detect proper concentration levels through aqueous media. A
sharper or narrower peak provides a greater chance to see the concentration dependence of
the absorption peak at that frequency because it is a better defined peak.
As we pointed out previously in figure 2 (b) we still have an extra feature near 5200 cm−1 ,
which has both a peak (on lower frequency side) and a dip (on higher frequency side). To
understand this feature we simulate it with Lorentzian (reference) peaks. We found that
there are three ways to produce such a feature. We show results of the three ways in figure
3 (b), 3 (c) and 3 (d), respectively. In figure 3 (a) we show the reference Lorentzian peak
along with three peaks shifted the horizontal axis by ± 5 cm−1 and one shifted peak by -100
cm−1 . The Lorentzian peak can be described as follows:
Lpeak (ω) =
Γ/2
A
π (ω − ωc )2 + (Γ/2)2
(4)
where A is area under the peak, ωc is the center frequency of the peak, and Γ is the width
of the peak, which is the full width at half maximum (FWHM). In figure 3 (b) we show
difference between each shifted peak with various shifting amounts (ωshif t = -100, -5, -4, -3, 2, -1 and +5 cm−1 ) with a fixed width (Γ = 400 cm−1 ) and a fixed amplitude (A = 200 cm−2 )
and the reference peak; Lshif t (ω) − Lref (ω) = (A/π)(Γ/2){1/[(ω − ωshif t − ωc )2 + (Γ/2)2 ] −
1/[(ω − ωc )2 + (Γ/2)2 ]}. As we can see in the figure the more shifting produces the larger
and better defined difference spectra. We note that the difference between the peak and dip
positions do not change very much up to -100 cm−1 shift because of a large width 400cm−1 of
the peak; 243 cm−1 for -100 case and 230 cm−1 for -5 case. But more shifting causes the larger
interval between the peak and the dip. The frequency at the zero crossing is shifted by a half
the frequency shift amount; the difference for -100 cm−1 case the zero crossing frequency is
1150 cm−1 . In figure 3 (c) we show difference between each peak at 5195 cm−1 (i.e. ωshif t =
7
5 cm−1 ) with various amplitudes (A = 50, 100, 150 and 200 cm−2 ) and the reference peak;
Lamplitude (ω)−Lref (ω) = (A/π)(Γ/2){1/[(ω −ωshif t −ωc )2 +(Γ/2)2 ]−1/[(ω −ωc )2 +(Γ/2)2 ]},
where Γ = 400 cm−1 . Here we also change the amplitude of the reference peak according
to each peak amplitude. The results are shown in the figure; the more intense peaks give
the larger differences. We note that the peak and dip positions are not at all dependent
of the amplitude. In figure 3 (d) we show the difference between each broadened peak at
5195 cm−1 (i.e. ωshif t = 5 cm−1 ) with various widthes (Γ0 = 400, 450, 500, 550, 600, and
650 cm−1 ) and the reference peak; Lwidth (ω) − Lref (ω) = (A/π){(Γ0 /2)/[(ω − ωshif t − ωc )2 +
(Γ0 /2)2 ] − (Γ/2)/[(ω − ωc )2 + (Γ/2)2 ]}, where A = 200 cm−2 and Γ = 400 cm−1 . As we can
see in the figure the sharpest peak gives the largest and most-defined difference. We also
note that the peak (dip) position is red (blue) shifted as the width increases.
From observation of these three cases we can conclude that the extra feature in figure 2
(b) can be attributed to the second case i.e. amplitude changes with concentration. The
intensity of the sharp absorption band edge due to the interacting water around 5200 cm−1 is
getting larger as the amount of glucose increases, which is reasonable because more water
molecules get involved in the interaction with the glucose molecules as the concentration
increases. We do not expect a concentration dependent change in the frequency of the
interacting water as long as we keep a relatively low glucose concentration in the solution.
We fit the observed peak and dip feature near 5200 cm−1 in figure 2 (b) by using the
model of our second case. In figure 1 we show the reference water peak at 5210 cm−1 (green
dashed line), here we only considered the sharp absorption edge part of the water absorption
band near 5200 cm−1 .[22] In figure 2 (b) we show an example fit (green dashed line) to the
peak and dip feature near 5200cm in the 10 g/dL spectrum. We note that the amplitude (or
area) of the reference peak is 3300 cm−2 and its width is 170 cm−1 . From the fit we find that
the amount of red shift is quit small, ' 2 cm−1 . However, the resolution of the frequency
shifting depends on the width of the reference peak considered. In our case the width (170
cm−1 ) is quite large compared with the shift (2 cm−1 ) so it is not very resolvable. Still what
we can tell clearly is that the water absorption peak experiences a red shift. Here one may
wonder that the instrumental resolution used to collect the spectra is 5 cm−1 whereas the
observed shift in the water absorption band is around 2 cm−1 . However, we measure the
resulting feature from the shift, which is much broader (about the width of the reference
peak) than the instrumental resolution shown in the figure. We also expect to observe red
8
shifts from other water peaks. To show this we display the absorption of pure glucose and
the extracted glucose absorption spectrum, αsol (ω, C) − αw,def f (ω) for C = 10g/dL in a same
panel as shown in figure 4. In the figure we observe signatures of red shifts for other water
peaks clearly. The signatures, which are strong dips, appear near sharp edges for water
absorption namely, 3800 cm−1 , 5200 cm−1 , and 7000 cm−1 . So the red shifts seem to occur
for all water absorption peaks. Roughly, we can tell that the height of the peak or depth of
the dip of the feature can be a measure of the intensity of the interaction (see figure 3 (c)).
The resulting concentration dependent intensities of the red shift, height, and depth are
displayed in figure 5 (b). As we expected, the extracted intensity is roughly proportional to
the glucose concentration. The deviation from the linearity may come from the uncertainty
in the water subtraction procedure.
From the appropriate water subtraction procedure, which we described previously, we can
obtain the effective thickness of water for each glucose solution. Figure 5 (c) displays the
extracted effective thickness of water as a function of the glucose concentration. It shows a
strong linear relationship between the effective thickness and the concentration from 1 g/dL
through 10 g/dL. The water displacement coefficient is defined by the molar concentration
change of water caused by the dissolution of a unit molar concentration of the solute. The
molar concentration is defined by the number of moles per a liter of solvent (in our case,
water). More practically, the water displacement coefficient is the number of water molecules
which are replaced by a solute molecule in the solution. By using these definitions we can
write down the effective thickness of water in the cell as a function of glucose concentration.
h
def f (C) = d0 1 +
C0 ≡
C 0 · wdis i
and
1 + C 0 · wdis
Mwater
C
100 · Msolute
(5)
where C is the concentration in g/dL, def f (C) is the concentration dependent effective
thickness of water, Mwater is the molecular weight of water, Msolute is the molecular weight
of solute, d0 is the real thickness of the cell (in our case, 252 µm) and wdis is the water
displacement coefficient. We see that C 0 is a small quantity; 0.01 for 10 g/dL glucose
solution and 0.0053 for 10 g/dL sucrose solution, these are the maximum values for glucose
and sucrose solutions. The water displacement coefficient is roughly a single digit value. So
C 0 · wdis is small and we can rewrite the equation (5) approximately as follows:
def f (C) ∼
= d0 [1 + C 0 · wdis · (1 − C 0 · wdis )] or
9
def f (C) ' d0 [1 + C 0 · wdis ]
d0 · Mwater · wdis
= d0 +
C
100 · Msolute
(6)
In the lower equation we made a further approximation assuming C 0 wdis 1. This last
equation shows that def f (C) is linear in the concentration C, which is what we obtain from
our analysis and the results shown in figure 5 (c). We fit the data points in figure 5 (c) to a
straight line; def f (C) = 251.9 (± 0.8) + 1.490 (± 0.128) C (in µm). From the linear fitting we
obtain the real thickness of the cell and the slope of the straight line. By using the fitting
parameters we are able to estimate the water displacement coefficient of glucose.
wdis = slope
Msolute · 100
Mwater · d0
(7)
where slope is the slope of the straight line. The water displacement coefficient of glucose
obtained is 5.91 ± 0.51 at 23 ◦ C. This means that one glucose molecule can take up the
space of 5.91 water molecules in the solution. This value seems to be rather large compared
to a value of 5.051 at 21 ◦ C reported in Ref [23]. We also note that the relative standard
deviation for the proposed method is 8.6 % (0.51/5.051) compared to a value of 0.056
% (0.0035/6.245) from the direct density method reported in Ref [14]. The precision of
this method for obtaining the water displacement coefficient is not as good as that of the
density method. A new method introduced in the following paragraph allows us to obtain a
concentration dependent water displacement coefficient. The concentration dependent water
displacement coefficient of glucose (see lower figure 6) shows a better value for the coefficient
at high concentrations; for 10 g/dL sample, the water displacement coefficient is 5.10, which
seems to be a more reliable value for the coefficient at 23 ◦ C.
We also can obtain the water displacement coefficient from an another simpler method
as follows. By comparing intensities of an absorption peak of pure glucose (for example, at
4000 cm−1 ) in figure 1 and the corresponding peak of glucose alone in solution in figure 2
(b) we can estimate an effective thickness of glucose alone in solution compared to the total
thickness of the solution. If the total volume of the solution consists of glucose alone the
absorption coefficient of the solution sample would be identical to that of pure glucose. Since
the absorption intensity of glucose is proportional to the effective thickness (or amount) of
glucose alone in solution the intensity ratio is the same as the effective thickness ratio as
10
the following equation,
Asolute.sol
C/Msolute · wdis · NA
=
Asolute.pure
[100/Mwater + C/Msolute · wdis ] · NA
(8)
where Asolute.pure and Asolute.sol are the peak heights of pure glucose and glucose in solution,
respectively, C is the concentration in g/dL and NA is the Avogadro’s number. When we
solve for the water displacement coefficient, wdis , we get the following equation.
wdis =
Asolute.sol · 100 · Msolute
(Asolute.pure − Asolute.sol ) · C · Mwater
(9)
This equation means that for a given concentration, if we know the water displacement of solute and its absolute absorption coefficient we can easily estimate the absorption coefficient of
solute alone in solution. In other word if we can measure the absorption coefficient of solute
alone in solution for a given concentration we are able to obtain the water displacement coefficient of the solute. For example, we consider 10 g/dL glucose solution and the absorption
peak at 4000 cm−1 . Then by using eq. (9) wdis = (3.52×100×180)/[(72.5−3.52)×10×18] ∼
=
5.10. Even though the value is slightly smaller than the previously extracted value (5.91) it
is consistent with the previous one. The concentration dependent water displacement of glucose is shown in Fig. 6 along with the concentration dependent water coefficient of sucrose.
It seems to be independent of concentration even though there are some noisy data points
in the low concentration region due to the uncertainty in the water subtraction procedure.
The water displacement coefficient of glucose shows a strong temperature dependence;
5.051 at 21 ◦ C [23] and 6.245 at 37 ◦ C [14] and our extracted water displacement coefficients
of glucose seem to be consistent with other studies; at least our value is in between those two
values obtained at two lower and higher temperatures. The temperature dependence in the
water displacement coefficient probably comes mostly from thermally induced morphology
change of glucose molecules in the water. More systematic studies should be performed on
temperature dependent water displacement of glucose. We note that, at very high concentrations, the linear trend can not hold because interaction between nearest glucose molecules
which is an indirect repulsive interaction in water will become stronger as the concentration
increases.
We performed the same experiment and data analysis with a different solute, sucrose
(C12 H22 O11 ), which has a larger molecular weight. The measured data and analysis results
are displayed in figure 7, 8 and figure 9. Although there are some detailed qualitative
11
differences, the overall qualitative concentration dependent trends are very similar to those
of glucose. There are four sucrose absorption peaks in the combination region and two peaks
in the first overtone region as for glucose. One thing which we would like to note is that
the relative intensities between the peaks are different. As we can see in the pure sucrose
absorption spectrum, the peak at 4390 cm−1 is relatively large. The recovered concentration
dependent peak height of sucrose absorption modes in the combination region are displayed
in figure 9 (a). They show a linear dependence on the concentration as we expected. We
observe an additional feature other than sucrose absorption peaks in figure 8 (b) as those
in figure 2 (b). We show an example fit to the feature for 10 g/dL only for the absorption
edge region. From this fitting we get that the red shift is very small around 2 cm−1 . The
concentration dependent height and depth of the feature are shown in figure 9 (b). This
indicates that water molecules around a sucrose molecule is not free; the absorption peaks
due to the water will be shifted to lower frequencies, i.e. red shifts, which is due to water
structure enhancement within the hydration shells around solute molecules.[20, 21]
We also display the concentration dependent effective thickness,
water in the liquid cell in figure 9 (c).
def f (C),
of
We fit the data to a straight line;
def f (C) = 252.3 (± 0.4) + 1.427 (± 0.065) C (in µm). By using eq. (7), and the extracted slope of the line and d0 from the fit we can get the water displacement coefficient
of sucrose, 10.76 ± 0.46 at 23 ◦ C. The water displacement coefficient tells us that a sucrose
molecule can take up space equivalent to 10.76 water molecules in the solution. We also
used the other method (see eq. (9)) to obtain the water displacement coefficient of sucrose.
For example, we consider the 10g/dL sucrose solution and the absorption peak at 4000
cm−1 . Then by using eq. (9), wdis = (3.57 × 100 × 342)/[(72.0 − 3.57) × 10 × 18] ∼
= 9.35.
Even though the value is slightly smaller than the previously extracted value (10.76) it is
quite consistent with the previous one. The concentration dependent water displacement
of sucrose is shown in Fig. 6. In low concentration region the data show more noise and
seem to deviate from the concentration independent trend at high concentration due to the
uncertainty in the water subtraction procedure in the low concentration region. The molecular weight of sucrose (Msucrose = 342) is almost twice of glucose (Mglucose = 180) i.e. in
solution a sucrose molecule also takes up almost twice the space of a glucose molecule. This
may indicate that sucrose molecules in solution have elongated shapes instead of global ones.
12
CONCLUSIONS
It is clear from our work as well as previous studies that water displacement is an important quantity that must be considered for a proper study of glucose concentration in aqueous
media and blood. Our new method is fundamentally different from the study of Amerov,
Chen, and Arnold, who realized the problem introduced by water displacement and compensated for it by using an independently measured water displacement coefficient based
on density measurements.[14] We introduce a new spectroscopic method which is simple
where we remove water absorption bands accurately from measured glucose aqueous solutions without independent measurement of water displacement by the glucose. Using the
linear relationship on concentration found for the effective thickness of water in the liquid
cell we can properly manipulate the spectra to remove water absorption and obtain reliable
concentration dependent glucose absorption bands. In the spectra obtained from the subtraction procedure we observed signatures of interaction between water and solute molecules
in the solution. The red shift of the water absorption near 5200 cm−1 is around 2 cm−1 ,
which is very small but clearly observable in the spectra. As we mentioned previously, the
amount of shifting is not easily resolvable since the width of water absorption is quite broad
compared with the red shift. Additionally, we were able to extract the water displacement
coefficient of glucose, which is consistent with values reported in literatures.[14, 23] These
results may help to monitor non-invasively the glucose level in human body.
This method has several advantages: first of all, by removing the need to measure the
water displacement coefficient independently, we can estimate a reliable water displacement coefficient from our concentration dependent spectrum, making it a self-consistent
method which we can apply to other solutions.
Actually, we also applied the same
method to sucrose aqueous solution and got a reasonable water displacement coefficient
of sucrose. The method of water displacement extraction in this paper can provide as a
new general method using optical spectroscopy technique for other biological or organic
materials.
This method also allows us to observe red shifts in the difference spectra,
which is not easy to detect with different experimental techniques. Similar red shifts were
observed by other groups and other experimental techniques in different aqueous solutions,
or water-oil and water-air interfaces. [18, 19] Our approach provides another useful tool
to study water molecules in the hydration cell around a solute molecule in aqueous solutions.
13
Acknowledgement We thank T. Timusk and R. Peters for useful discussions. This work
has been supported by the special fund of Department of Physics at Pusan National University, Busan, Republic of Korea. This work also was supported by the National Research
Foundation of Korea Grant funded by the Korean Government (NRF-2010-371-B00008).
14
(a)
1 g/dL
-1
α sol(ω,C) - αw,d (ω) (cm )
2
0
0
-2
-4
-6
glucose 1 g/dL (0.056 M)
glucose 2 g/dL (0.111 M)
glucose 4 g/dL (0.222 M)
glucose 6 g/dL (0.333 M)
glucose 8 g/dL (0.444 M)
glucose 10 g/dL (0.556 M)
10 g/dL
-8
0.4
10 g/dL
0.2
eff
-1
α sol(ω,C) - αw,d (ω) (cm )
3
2
0.0
-0.2
1
6000
7000
0
1 g/dL
-1
pure glucose (x 1/22)
fit (see figure 3 (b))
-2
(b)
-3
4000
5000
6000
7000
-1
Frequency, ω (cm )
Fig. 2. (Color online) (a) Glucose absorption bands in solutions obtained at six different
concentrations by subtracting water spectrum from those of the glucose solutions. Water
displacement coefficient of glucose has not been considered on these spectra (see in the text).
(b) Glucose absorption coefficients in six different solutions. Water displacement effects have
been taken into account for the subtracting water absorption procedure (see in the text).
The green dotted line is a fitted line to the feature near 5200 cm−1 with both peak and dip
from a model calculation (see figure 3 (b) and corresponding text). The black dashed line in
the lower frame is the pure glucose absorption spectra with its intensity reduced by a factor
of 22. In the inset we display an expanded view to show spectral features better in the first
overtone region.
15
0.6
-1
Lpeak(ω)
(a)
0.4
reference with width 400 cm ; Lref(ω)
ctr freq. -100
0.34
ctr freq. -5
ctr freq. +5
0.32
0.30
0.28
0.2
0.26
Lwidth(ω) - Lref(ω) Lamplitude(ω) - Lref(ω)
Lshift(ω) - Lref(ω)
5150 5200 5250
0.0
0.010
(b)
-100 (x 0.1)
-100 (ctr freq.)
-5 (ctr freq.)
-4 (ctr freq.)
-3 (ctr freq.)
-2 (ctr freq.)
-1 (ctr freq.)
+5 (ctr freq.)
-5
0.005
0.000
-1
-0.005
0.010
(c)
-1
[width = 400 cm ]
-2
[amplitude = 200 cm ]
amp200
-5 (ctr. freq.), amp200
-5 (ctr. freq.), amp150
-5 (ctr. freq.), amp100
-5 (ctr. freq.), amp50
amp50
[ctr freq. = 5205 cm ]
-1
[width = 400 cm ]
0.005
0.000
-1
-0.005
0.010
(d)
-5 (ctr freq.), w400
-5 (ctr freq.), w450
-5 (ctr freq.), w500
-5 (ctr freq.), w550
-5 (ctr freq.), w600
-5 (ctr freq.), w650
w400
0.005
0.000
-1
[ctr freq. = 5205 cm ]
-2
[amplitude = 200 cm ]
w650
-0.005
4000
5000
6000
7000
-1
Frequency, ω (cm )
Fig. 3. (Color online) (a) We show a reference peak which has its center at 5200 cm−1 and
width 400 cm−1 . We also show two shifted peaks in horizontal direction by negative 5 cm−1
(dashed dotted red curve) and positive 5 cm−1 (dashed blue curve), respectively. In the inset
we expand the graphs near the peak region to show the shifts more clearly. (b) We also show
resulting differences subtracted the reference peak at 5200 cm−1 from the shifted peaks by
seven different amounts (see in the text). (c) We show resulting differences subtracted the
reference peak at 5200 cm−1 from the peaks at 5205 cm−1 with four different amplitudes
(see in the text). (d) (c) We show resulting differences subtracted the reference peak at 5200
cm−1 from the peaks at 5205 cm−1 with six different widths (see in the text).
16
5
α sol(ω,C) - αw,d (ω), C=10g/dL
eff
4
pure glucose (x 1/22)
water (x 1/40)
2
-1
α(ω) (cm )
3
1
0
-1
-2
-3
4000
5000
6000
7000
-1
Frequency, ω (cm )
Fig. 4. (Color online) Comparison the pure glucose absorption and the extracted glucose
absorption (αsol (ω, C) − αw,def f (ω)) from 10g/dL solution. We note that we reduce the
intensity of the pure glucose absorption by a factor of 22. We also show the water spectrum
as well for comparison purpose and reduce its intensity by a factor of 40.
17
-1
height or depth (cm ) peak height (cm-1)
deff (C) (µm)
4
-1
(a)
4000 cm
-1
4280 cm
-1
4386 cm
-1
4757 cm
(b)
Depth
Height
(c)
Effective Thickness
linear fit:
deff (C) = 251.9 + 1.490 C (µm)
3
2
1
0
2.5
2.0
1.5
1.0
0.5
0.0
270
265
260
d0 = 252 µm
wdis = 5.91
255
250
0
2
4
6
8
10
Concentration, C (g/dL)
Fig. 5. (Color online) (a) The concentration dependent peak height of four absorption modes
of glucose in the combination region. (b) The concentration dependent height and depth of
the new feature in figure 2 (b). (c) Concentration dependent effective thickness of the cell
extracted from the water subtraction procedure (see in the text). We observe a strong linear
relationship between the effective thickness of water and the glucose concentration.
18
15
wdis: sucrose
wdis: glucose
wdis(C)
10
5
0
0
2
4
6
8
10
Concentration, C (g/dL)
Fig. 6. (Color online) We display the concentration dependent water displacement of glucose
and sucrose obtained by using eq. 9.
150
130
A
water
sucrose 1 g/dL (0.029 M)
sucrose 2 g/dL (0.058 M)
sucrose 4 g/dL (0.117 M)
sucrose 6 g/dL (0.175 M)
sucrose 8 g/dL (0.234 M)
sucrose 10 g/dL (0.292 M)
pure sucrose
-1
water peak @ 5210 cm
120
110
5150
5200
-1
α(ω) (cm )
5100
100
30
50
B
27
24
4700
4750
4800
0
4000
5000
6000
7000
-1
Frequency, ω (cm )
Fig. 7. (Color online) Absorption coefficients of a pure amorphous sucrose (dotted dark
blue) a pure water (dash-dotted orange), and six glucose aqueous solutions (from top to
bottom; from low to high concentrations). We also show a water peak at 5200 cm−1 . In the
inset A and B we show expanded views near 5150 cm−1 and 4750 cm−1 respectively.
19
(a)
1 g/dL
-1
α sol(ω,C) - αw,d (ω) (cm )
2
0
0
-2
-4
-6
sucrose 1 g/dL (0.029 M)
sucrose 2 g/dL (0.058 M)
sucrose 4 g/dL (0.117 M)
sucrose 6 g/dL (0.175 M)
sucrose 8 g/dL (0.234 M)
sucrose 10 g/dL (0.292 M)
10 g/dL
-8
0.8
10 g/dL
0.4
eff
-1
α sol(ω,C) - αw,d (ω) (cm )
3
2
0.0
1
5500
6000
6500
7000
0
-1
1 g/dL
pure sucrose (x 1/20)
fit (see figure 2 (b))
-2
(b)
-3
4000
5000
6000
7000
-1
Frequency, ω (cm )
Fig. 8. (Color online) (a) Sucrose absorption bands in solutions obtained at six different
concentrations by subtracting water spectrum from those of the sucrose solutions. Water
displacement coefficient of sucrose has not been considered on these spectra (see in the text).
(b) Sucrose absorption coefficients in six different solutions. Water displacement effects have
been accounted for the subtracting procedure (see in the text). The black dashed line in the
lower frame is the pure glucose absorption spectra with its intensity reduced by a factor of
20. In the inset we display an expanded view to show spectral features better in the first
overtone region.
20
-1
height or depth (cm )
4007 cm
-1
4297 cm
-1
4388 cm
-1
4767 cm
3
2
1
0
(b)
2.5
Depth
Height
2.0
1.5
1.0
0.5
0.0
(c)
270
deff (C) (µm)
-1
(a)
-1
peak height (cm )
4
Effective Thickness
linear fit:
deff (C) = 252.3 + 1.427 C (µm)
265
260
d0 = 252 µm
wdis = 10.76
255
250
0
2
4
6
8
10
Concentration, C (g/dL)
Fig. 9. (Color online) (a) The concentration dependent peak height of four absorption modes
of sucrose in the combination region. (b) The concentration dependent height and depth of
the new feature in figure 8 (b). (c) Concentration dependent effective thickness of water.
We observe a strong linear relationship between the effective thickness of water and the
concentration.
21
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23
List of Figure Captions
Fig. 1. Absorption coefficients of a pure amorphous glucose (dotted dark blue line) a pure
water (dash-dotted orange line), and six glucose aqueous solutions (from top to bottom;
from low to high concentrations). We also show a water peak at 5200 cm−1 . In the inset A
and B we show expanded views near 5150 cm−1 and 4750 cm−1 respectively.
Fig. 2. (a) Glucose absorption bands in solutions obtained at six different concentrations
by subtracting water spectrum from those of the glucose solutions. Water displacement
coefficient of glucose has not been considered on these spectra (see in the text). (b) Glucose
absorption coefficients in six different solutions. Water displacement effects have been taken
into account for the subtracting water absorption procedure (see in the text). The green
dotted line is a fitted line to the feature near 5200 cm−1 with both peak and dip from a
model calculation (see figure 3 (b) and corresponding text). The black dashed line in the
lower frame is the pure glucose absorption spectra with its intensity reduced by a factor of
22. In the inset we display an expanded view to show spectral features better in the first
overtone region.
Fig. 3. (a) We show a reference peak which has its center at 5200 cm−1 and width 400
cm−1 . We also show two shifted peaks in horizontal direction by negative 5 cm−1 (dashed
dotted red curve) and positive 5 cm−1 (dashed blue curve), respectively. In the inset we
expand the graphs near the peak region to show the shifts more clearly. (b) We also show
resulting differences subtracted the reference peak at 5200 cm−1 from the shifted peaks by
seven different amounts (see in the text). (c) We show resulting differences subtracted the
reference peak at 5200 cm−1 from the peaks at 5205 cm−1 with four different amplitudes
(see in the text). (d) (c) We show resulting differences subtracted the reference peak at
5200 cm−1 from the peaks at 5205 cm−1 with six different widths (see in the text).
Fig. 4. Comparison the pure glucose absorption and the extracted glucose absorption
(αsol (ω, C) − αw,def f (ω)) from 10g/dL solution. We note that we reduce the intensity of the
pure glucose absorption by a factor of 22. We also show the water spectrum as well for
comparison purpose and reduce its intensity by a factor of 40.
24
Fig. 5. (a) The concentration dependent peak height of four absorption modes of glucose
in the combination region.
(b) The concentration dependent height and depth of the
new feature in figure 2 (b). (c) Concentration dependent effective thickness of the cell
extracted from the water subtraction procedure (see in the text). We observe a strong
linear relationship between the effective thickness of water and the glucose concentration.
Fig. 6. We display the concentration dependent water displacement of glucose and sucrose
obtained by using eq. (9).
Fig. 7. Absorption coefficients of a pure amorphous sucrose (dotted dark blue) a pure
water (dash-dotted orange), and six glucose aqueous solutions (from top to bottom; from
low to high concentrations). We also show a water peak at 5200 cm−1 . In the inset A and
B we show expanded views near 5150 cm−1 and 4750 cm−1 respectively.
Fig. 8. (a) Sucrose absorption bands in solutions obtained at six different concentrations
by subtracting water spectrum from those of the sucrose solutions. Water displacement
coefficient of sucrose has not been considered on these spectra (see in the text). (b) Sucrose
absorption coefficients in six different solutions. Water displacement effects have been
accounted for the subtracting procedure (see in the text). The black dashed line in the
lower frame is the pure glucose absorption spectra with its intensity reduced by a factor of
20. In the inset we display an expanded view to show spectral features better in the first
overtone region.
Fig. 9. (a) The concentration dependent peak height of four absorption modes of sucrose
in the combination region. (b) The concentration dependent height and depth of the new
feature in figure 8 (b). (c) Concentration dependent effective thickness of water. We observe
a strong linear relationship between the effective thickness of water and the concentration.
25